An electron is accelerated from rest through potential difference $V$ and then enters a region of uniform magnetic field, where it undergoes uniform circular motion. The radius $r$ of the path and the difference in potential V are found to follow the empirical law $r=5{10}^{-5}\sqrt[\phantom{2}]{V},$ where $r$ and $V$ are expressed in meters and volts respectively. Calculate the magnitude of the magnetic field and the time the electron spends to make a $90$ turn. The mass of the electron is $m=9\mathrm{.}11{10}^{-31}kg.$